Set 1: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. We need to solve $-16 t^2 + 32 t + 10 = 0$. 1. Discriminant: $32^2 - 4(-16)(10) = 1024 + 640 = 1664$. 2. Formula: $t = \frac{-32 \pm \sqrt{1664}}{-32}$. 3. Approximate $\sqrt{1664} \approx 40.8$. 4. $t \approx \frac{-32 \pm 40.8}{-32}$. * Case 1: $(-72.8)/-32 \approx 2.275$ * Case 2: $(8.8)/-32 \approx -0.275$ (Time cannot be negative) So, $t \approx 2.28$ seconds. Choice B is incorrect because $t=1$ is the time of maximum height (vertex). Choice C is incorrect because it corresponds to the negative root magnitude. Choice D is incorrect because it is too large.